Results 1  10
of
43
Efficient DescriptorVector Multiplications in Stochastic Automata Networks
, 1996
"... This paper examines numerical issues in computing solutions to networks of stochastic automata. It is wellknown that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrixvector multi ..."
Abstract

Cited by 93 (15 self)
 Add to MetaCart
This paper examines numerical issues in computing solutions to networks of stochastic automata. It is wellknown that when the matrices that represent the automata contain only constant values, the cost of performing the operation basic to all iterative solution methods, that of matrixvector multiply, is given by ae N = N Y i=1 n i \Theta N X i=1 n i ; where n i is the number of states in the i th automaton and N is the number of automata in the network. We introduce the concept of a generalized tensor product and prove a number of lemmas concerning this product. The result of these lemmas allows us to show that this relatively small number of operations is sufficient in many practical cases of interest in which the automata contain functional and not simply constant transitions. Furthermore, we show how the automata should be ordered to achieve this.
Numerical Analysis of Superposed GSPNs
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 1996
"... The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representa ..."
Abstract

Cited by 63 (9 self)
 Add to MetaCart
The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized stochastic Petri nets (SGSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory efficient representation of iteration vectors as well as to a memory efficient structured representation of Q. In consequence the new algorithm is able to solve models which have state spaces with several millions of states, where other exact numerical methods become impracticable on a common workstation.
An Efficient Algorithm for Aggregating PEPA Models
 IEEE Transactions on Software Engineering
, 1999
"... Performance Evaluation Process Algebra (PEPA) is a formal language for performance modelling based on process algebra. It has previously been shown that using the process algebra apparatus compact performance models can be derived which retain the essential behavioural characteristics of the modelle ..."
Abstract

Cited by 52 (26 self)
 Add to MetaCart
Performance Evaluation Process Algebra (PEPA) is a formal language for performance modelling based on process algebra. It has previously been shown that using the process algebra apparatus compact performance models can be derived which retain the essential behavioural characteristics of the modelled system. However no efficient algorithm for this derivation was given. In this paper we present an efficient algorithm which recognises and takes advantage of symmetries within the model and avoids unnecessary computation. The algorithm is illustrated by a multiprocessor example. Keywords: Performance modelling, model aggregation, performance evaluation tools, stochastic process algebras. 1 Introduction In recent years several Markovian process algebras (MPAs) have been presented in the literature. These include PEPA [1], MTIPP [2], and EMPA [3]. As with classical process algebras, these formalisms allow models of systems to be constructed which are amenable to functional or behavioural an...
A Simple Time Scale Decomposition Technique for Stochastic Process Algebras
 The Computer Journal
, 1995
"... this paper we present cases when this structure may be used to inform the solution of the model, leading to an efficient solution based on a decomposition of the underlying Markov process. The decomposition which we consider is time scale decomposition, based on Courtois's ..."
Abstract

Cited by 26 (16 self)
 Add to MetaCart
this paper we present cases when this structure may be used to inform the solution of the model, leading to an efficient solution based on a decomposition of the underlying Markov process. The decomposition which we consider is time scale decomposition, based on Courtois's
A toolbox for functional and quantitative analysis of DEDS
 Proc. 10th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, Lecture Notes in Computer Science 1469
, 1998
"... Abstract This paper presents a toolbox for the construction of modular tools for functional and quantitative (performance) analysis of discrete event dynamic systems (DEDS). The intention is to simplify the usage of appropriate analysis algorithms, thus supporting the development of appropriate tool ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
Abstract This paper presents a toolbox for the construction of modular tools for functional and quantitative (performance) analysis of discrete event dynamic systems (DEDS). The intention is to simplify the usage of appropriate analysis algorithms, thus supporting the development of appropriate tools.
Exploiting Quasireversible Structures in Markovian Process Algebra Models
 Special Issue: Proc. of 3rd Process Algebra and Performance Modelling Workshop
"... this paper we exploit results from queueing networks to identify a restricted form of interaction between suitable MPA components which leads to a product form solution. Each component of the model may be solved separately and the compositional structure of an MPA consequently facilitates efficient ..."
Abstract

Cited by 23 (10 self)
 Add to MetaCart
this paper we exploit results from queueing networks to identify a restricted form of interaction between suitable MPA components which leads to a product form solution. Each component of the model may be solved separately and the compositional structure of an MPA consequently facilitates efficient solution for successively more complex models. This work uses the notion of quasireversibility
Stochastic Process Algebras as a Tool for Performance and Dependability Modelling
 In Proc. of IEEE International Computer Performance and Dependability Symposium
, 1995
"... The stochastic processalgebra modellingparadigm has been introduced recently as an extension of classical process algebras with timing information aiming mainly at the integration of functional design with quantitative analysis of computer systems. Time is represented by exponentially distributed r ..."
Abstract

Cited by 21 (12 self)
 Add to MetaCart
The stochastic processalgebra modellingparadigm has been introduced recently as an extension of classical process algebras with timing information aiming mainly at the integration of functional design with quantitative analysis of computer systems. Time is represented by exponentially distributed random variables that are assigned to each activity in the model. Thus, the semantic model of a stochastic processalgebra model can easily be transformed into a continuous time Markov chain which is suitable for computing performance measures as well as dependability measures. The main problem that one encounters frequently in Markov based modelling is the problem of having to solve a huge and stiff Markov chain. In dependability modelling, largeness is caused by lots of detailed and sometimes surplus information stored in the high level model. Stiff Markov chains result when one uses performance related activities together with reliability events in the same model. Various methods to tackle...
Exploiting Structure in Solution: Decomposing Composed Models
 Proceedings of 6th International Workshop on Process Algebra and Performance Modelling
, 1998
"... Since their introduction nearly ten years ago, compositionality has been reported as one of the major attractions of stochastic process algebras. The benefits that compositionality provides for model construction are readily apparent and have been demonstrated in numerous case studies. Early researc ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
Since their introduction nearly ten years ago, compositionality has been reported as one of the major attractions of stochastic process algebras. The benefits that compositionality provides for model construction are readily apparent and have been demonstrated in numerous case studies. Early research on the compositionality of the languages focussed on how the inherent structure could be used, in conjunction with equivalence relations, for model simplification and aggregation. In this paper we consider how far we have been able to take advantage of compositionality when it comes to solving the Markov process underlying a stochastic process algebra model and outline directions for future work in order for current results to be fully exploited. 1 Introduction Stochastic process algebras (SPA) were first proposed as a tool for performance and dependability modelling in 1989 [24]. At that time there was already a plethora of techniques for constructing performance models so the introducti...
Extracting passage times from PEPA models with the HYDRA tool: A case study
 UNIVERSITY OF WARWICK
, 2003
"... Passage time densities and quantiles are important performance metrics which are increasingly used in specifying service level agreements (SLAs) and benchmarks. PEPA is a popular stochastic process algebra and a powerful formalism for describing performance models of communication and computer syst ..."
Abstract

Cited by 16 (10 self)
 Add to MetaCart
Passage time densities and quantiles are important performance metrics which are increasingly used in specifying service level agreements (SLAs) and benchmarks. PEPA is a popular stochastic process algebra and a powerful formalism for describing performance models of communication and computer systems. We present a case study passage time analysis of an 82,944 state PEPA model using the HYDRA tool. HYDRA specialises in passage time analysis of large Markov systems based on stochastic Petri nets. By using the new Imperial PEPA compiler (ipc), we can construct a HYDRA model from a PEPA model and obtain passage time densities based on the original PEPA description.
Semantics for Structured Systems Modelling and Simulation
"... Simulation modelling is an important tool for exploring and reasoning about complex systems. Many supporting languages are available. Commonly occurring features of these languages are constructs capturing concepts such as process, resource, and location. We describe a mathematical framework that su ..."
Abstract

Cited by 16 (12 self)
 Add to MetaCart
Simulation modelling is an important tool for exploring and reasoning about complex systems. Many supporting languages are available. Commonly occurring features of these languages are constructs capturing concepts such as process, resource, and location. We describe a mathematical framework that supports a modelling idiom based on these core concepts, and which adopts stochastic methods for representing the environments within which systems exist. We explain how this framework can be used to give a semantics to a simulation modelling language, Core Gnosis, that includes basic constructs for process, resource, and location. We include a brief discussion of a logic for reasoning about models that is compositional with respect to their structure. Our mathematical analysis of systems in terms of process, resource, location, and stochastic environment, together with a language that captures these concepts quite directly, yields an efficient and robust modelling framework within which natural mathematical reasoning about systems is captured.